GigaMesh

Multi-scale integral invariants for robust character extraction from irregular polygon mesh data. Hundreds of thousands of ancient documents with cuneiform script are known to be in museum collections and are found on a daily basis at archaeological excavations. Analyzing these documents is essential to understand the origins of civilization, legislation and religion. This script is a handwriting and was used for several millennia in the ancient Middle East. Its name is derived from the Latin word for wedge, which is the 3D-shape left by an ancient scribe’s stylus, when it was pressed into the soft surface of a clay tablet. Manually drawing and transcribing these tablets is a laborious and tedious task and assistance by an automated and computerized system is highly demanded. The aim of this thesis is extracting these handwritten characters, i.e. 3D-shapes with high variability. The crucial steps for feature extraction from 2D-manifolds in 3D-space are reliable edge detection and segmentation. This can be achieved using integral invariant filtering, a robust technique known from signal processing and shape matching in 2D-space. In 3D-space the state-of-the-art systems roughly estimate integral invariants for determining small numbers of highly distinctive features to solve puzzles of fractured objects. In order to precisely determine 3D-shapes of characters the pipeline known from image processing and pattern recognition is adapted for 3D-models. These models have millions of vertices, which are acquired by optical 3D-scanners. The vertices approximate manifolds with an irregular triangular mesh. Different types of integral invariant filtering in multiple scales lead to different high-dimensional feature spaces. Convolutions and combined metrics are applied to the feature spaces to determine connected components i.e. characters with sub-triangle accuracy within a manifold. Concurrently with the design of novel algorithms, the properties of the integral invariants are investigated. Understanding these properties is highly relevant for robust curvature measures and segmentation. The extraction of characters is completed with a Voronoi inspired method resulting in a minimal meaningful vector representation. This representation is an important basis for paleography. Further abstraction and normalization lead to character recognition. The embedment of the proposed methods in the novel and layered GigaMesh software framework enables a wide variety of applications. Memory efficiency and parallel processing were taken into account in the design of the configurable mesh processing pipeline. The pipeline has only one relevant parameter, which is the maximum size of the expected features. The proposed methods were tested on hundreds of cuneiform tablets as well as on other objects including synthetic datasets. Representative results are shown and an evaluation regarding accuracy and performance of the algorithms are given. Finally observations about integral invariants in higher dimensions are shown and an outlook is given.